A First Course in Probability (10th Edition)

10th Edition

ISBN: 9780134753119

Author: Sheldon Ross

Publisher: PEARSON

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Textbook Question

Chapter 5, Problem 5.37P

Suppose that the life distribution of an item has the hazard rate function λ ( t ) = t 3 , t > 0 . What is the probability that

a. the item survives to age 2?

b. the item’s lifetime is between .4 and 1.4?

c. a 1-year-old item will survive to age 2?

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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Chapter 5, Problem 5.36P

Chapter 5, Problem 5.38P

Chapter 5 Solutions

A First Course in Probability (10th Edition)

Ch. 5 - Let X be a random variable with probability...Ch. 5 - Prob. 5.2P Ch. 5 - Prob. 5.3P Ch. 5 - The probability density function of X. the...Ch. 5 - Prob. 5.5P Ch. 5 - Compute E[X] if X has a density function given by...Ch. 5 - The density function of X is given by...Ch. 5 - The lifetime in hours of an electronic tube is a...Ch. 5 - Consider Example 4b &I of Chapter 4 &I, but now...Ch. 5 - Trains headed for destination A arrive at the...

Ch. 5 - A point is chosen at random on a line segment of...Ch. 5 - A bus travels between the two cities A and B....Ch. 5 - You arrive at a bus stop at 10A.M., knowing that...Ch. 5 - Let X be a uniform (0, 1) random variable. Compute...Ch. 5 - If X is a normal random variable with parameters...Ch. 5 - The annual rainfall (in inches) in a certain...Ch. 5 - The salaries of physicians in a certain speciality...Ch. 5 - Suppose that X is a normal random variable with...Ch. 5 - Let be a normal random variable with mean 12 and...Ch. 5 - If 65 percent of the population of a large...Ch. 5 - Suppose that the height, in inches, of a...Ch. 5 - Every day Jo practices her tennis serve by...Ch. 5 - One thousand independent rolls of a fair die will...Ch. 5 - The lifetimes of interactive computer chips...Ch. 5 - Each item produced by a certain manufacturer is,...Ch. 5 - Two types of coins are produced at a factory: a...Ch. 5 - In 10,000 independent tosses of a coin, the coin...Ch. 5 - Twelve percent of the population is left handed....Ch. 5 - A model for the movement of a stock supposes that...Ch. 5 - An image is partitioned into two regions, one...Ch. 5 - a. A fire station is to be located along a road of...Ch. 5 - The time (in hours) required to repair a machine...Ch. 5 - If U is uniformly distributed on (0,1), find the...Ch. 5 - Jones figures that the total number of thousands...Ch. 5 - Prob. 5.35P Ch. 5 - The lung cancer hazard rate (t) of a t-year-old...Ch. 5 - Suppose that the life distribution of an item has...Ch. 5 - If X is uniformly distributed over (1,1), find (a)...Ch. 5 - Prob. 5.39P Ch. 5 - If X is an exponential random variable with...Ch. 5 - If X is uniformly distributed over(a,b), find a...Ch. 5 - Prob. 5.42P Ch. 5 - Find the distribution of R=Asin, where A is a...Ch. 5 - Let Y be a log normal random variable (see Example...Ch. 5 - The speed of a molecule in a uniform gas at...Ch. 5 - Show that E[Y]=0P{Yy}dy0P{Yy}dy Hint: Show that...Ch. 5 - Show that if X has density function f. then...Ch. 5 - Prob. 5.4TE Ch. 5 - Use the result that for a nonnegative random...Ch. 5 - Prob. 5.6TE Ch. 5 - The standard deviation of X. denoted SD(X), is...Ch. 5 - Let X be a random variable that takes on values...Ch. 5 - Show that Z is a standard normal random variable;...Ch. 5 - Let f(x) denote the probability density function...Ch. 5 - Let Z be a standard normal random variable Z and...Ch. 5 - Use the identity of Theoretical Exercises 5.5 .Ch. 5 - The median of a continuous random variable having...Ch. 5 - The mode of a continuous random variable having...Ch. 5 - If X is an exponential random variable with...Ch. 5 - Compute the hazard rate function of X when X is...Ch. 5 - If X has hazard rate function X(t), compute the...Ch. 5 - Prob. 5.18TE Ch. 5 - If X is an exponential random variable with mean...Ch. 5 - Prob. 5.20TE Ch. 5 - Prob. 5.21TE Ch. 5 - Compute the hazard rate function of a gamma random...Ch. 5 - Compute the hazard rate function of a Weibull...Ch. 5 - Prob. 5.24TE Ch. 5 - Let Y=(Xv) Show that if X is a Weibull random...Ch. 5 - Let F be a continuous distribution function. If U...Ch. 5 - If X is uniformly distributed over (a,b), what...Ch. 5 - Consider the beta distribution with parameters...Ch. 5 - Prob. 5.29TE Ch. 5 - Prob. 5.30TE Ch. 5 - Prob. 5.31TE Ch. 5 - Let X and Y be independent random variables that...Ch. 5 - Prob. 5.33TE Ch. 5 - The number of minutes of playing time of a certain...Ch. 5 - For some constant c. the random variable X has the...Ch. 5 - Prob. 5.3STPE Ch. 5 - Prob. 5.4STPE Ch. 5 - The random variable X is said to be a discrete...Ch. 5 - Prob. 5.6STPE Ch. 5 - To be a winner in a certain game, you must be...Ch. 5 - A randomly chosen IQ test taker obtains a score...Ch. 5 - Suppose that the travel time from your home to...Ch. 5 - The life of a certain type of automobile tire is...Ch. 5 - The annual rainfall in Cleveland, Ohio, is...Ch. 5 - Prob. 5.12STPE Ch. 5 - Prob. 5.13STPE Ch. 5 - Prob. 5.14STPE Ch. 5 - The number of years that a washing machine...Ch. 5 - Prob. 5.16STPE Ch. 5 - Prob. 5.17STPE Ch. 5 - There are two types of batteries in a bin. When in...Ch. 5 - Prob. 5.19STPE Ch. 5 - For any real number y define byy+=y,ify00,ify0 Let...Ch. 5 - With (x) being the probability that a normal...Ch. 5 - Prob. 5.22STPE Ch. 5 - Letf(x)={13ex1313e(x1)ifx0if0x1ifx1 a. Show that f...Ch. 5 - Prob. 5.24STPE

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Suppose that the life distribution of an item has the hazard rate function λ ( t ) = t 3 , t &gt; 0 . What is the probability that a. the item survives to age 2? b. the item’s lifetime is between .4 and 1.4? c. a 1-year-old item will survive to age 2?

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Chapter 5 Solutions

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Suppose that the life distribution of an item has the hazard rate function λ ( t ) = t 3 , t > 0 . What is the probability that a. the item survives to age 2? b. the item’s lifetime is between .4 and 1.4? c. a 1-year-old item will survive to age 2?